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For a mixed quantum state with density matrix $\rho$ there are infinitelymany ensembles of pure quantum states, which average to $\rho$. Starting fromLaplace principle of insufficient reason (not to give \emph{a priori}preference to any particular state), we derive a `natural' distribution of purestates averaging to $\rho$, which is `more spread' than all the others.

Guessing Quantum Ensemble Using Laplace Principle